Rusty Bowers was hoping to fight for election to the Arizona state senate, but lost the party's primary vote to David Farnsworth.
The staunch conservative also testified against Mr Trump to the committee investigating last year's Capitol riot.
Republican voters elsewhere in the US also backed Trump-endorsed candidates.
Candidates were chosen in a number of states on Tuesday following primary elections that decide who will stand for the party in November's mid-terms.
Those who have publicly supported Donald Trump and repeated his false claims about fraud and malpractice in the 2020 presidential election performed well.
It was a clear indication of Mr Trump's continuing influence on the Republican Party and the enduring support for his claims about the election he lost to President Joe Biden.
Mr Trump, who has hinted publicly at potentially running for president again, has endorsed dozens of Republican candidates.
Mr Bowers, 69, gave emotional testimony to the committee investigating the January 6 attack on the US Capitol in which he said Mr Trump and his adviser Rudy Giuliani tried to push him to help overturn the election results.
Afterwards, the Arizona Republican party - which has shifted steadily rightwards and is reliably pro-Trump - formally censured Mr Bowers, saying that he was "unfit to serve" the party and no longer a Republican "in good standing".
Mr Trump endorsed his challenger, and dismissed Mr Bowers as a "Rino" - Republican in name only - a favoured term of Mr Trump's for members of his party who refuse to back his false claims of election fraud.
Mr Farnsworth, a 71-year-old former state senator, received the backing of a number of Mr Trump's top allies. He has claimed the 2020 election was influenced by "a real conspiracy headed up by the devil himself".
Also in Arizona, which is a key battleground state, Mark Finchem - an election result denier who protested outside the Capitol on 6 January 2021 - won the Republican nomination for secretary of state.
And Blake Masters, a venture capitalist backed by Mr Trump and the technology entrepreneur Peter Thiel, captured the party's nomination to run for Arizona's US Senate seat against Democrat Mark Kelly in November.
In Michigan, Trump-endorsed candidate Tudor Nixon won the Republican nomination for governor. She will now face Democratic Governor Gretchen Whitmer, an outspoken Trump opponent, later this year.
Also in Michigan, Peter Meijer, one of 10 House Republicans who voted to impeach Mr Trump last year, lost to John Gibbs who served as Mr Trump's Assistant Housing Secretary. He has repeated the former president's false claims of election fraud and has said the 2020 election results were "mathematically impossible".
Elsewhere, Washington Representative Dan Newhouse and Jaime Herrera Beutler of Washington, Republicans who also voted to impeach Mr Trump, were fighting for their political lives.
Kansas Attorney General Derek Schmidt, endorsed by Mr Trump, secured the Republican nomination for governor.
But also in the state, Secretary of State Scott Schwab, a Republican who has opposed Mr Trump, successfully fought off a primary challenge from Mike Brown, a former county commissioner, who has spread false claims about the 2020 election.
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